The construct of emotional intelligence (EI) has gained increasing popularity over the last 10 years and now has a relatively large academic and popular associated literature. EI is beginning to be discussed within the medical education literature, where, however, it is treated uncritically. This reflections paper aims to stimulate thought about EI and poses the question: Are we trying to measure the unmeasurable? The paper begins with an outline of the relevance and meaningfulness of the topic of EI for doctors. It continues with an overview of the main models and measures of EI. We then critique the psychometric properties of EI measures and give an illustrative case study where we tested the psychometric properties of the ECI-U with medical students. After our critique, we present an alternative model of EI and outline possible future directions for educational research.